February i, 1894] 



NA TURE 



329 



so far as observation goes, all legitimate conclusions seem to 

 be against it. No induction of physical science is more uni- 

 versal or complete than that three conditions fix the position of 

 a point. The phenomena of light shows that no vibrations go 

 outside of three-dimensional space, even in the luminiferous 

 ether. If there is another universe, or a great number of other 

 universes, outside of our own, we can only say that we have no 

 evidence of their e.\erting any action upon our own. True, 

 those who are fond of explaining anomalous occurrences, by the 

 action of beings that we otherwise know nothing about, have 

 here a very easy field for their imagination. The question of 

 the sufiSciency of the laws of nature to account for all pheno- 

 mena is, however, too wide a one to be discussed at present. 



As illustrating the limitation of our faculties in this direction, 

 it is remarkable that we are unable to conceive of a space of 

 two dimensions otherwise than as contained in one of three. 

 A mere plane, with nothing on each side of it, is to us incon- 

 ceivable. We are thus compelled, so far as our conceptions go, 

 to accept three dimensions and no more. We have in this a 

 legitimate result of the universal experience through all genera- 

 tions being that of a triply extended space. 



Intimately associated with this is the concept of what is some- 

 times called curved space. I confess that I do not like this 

 expression, as I do not see how space itself can be regarded as 

 curved. Geometry is not the science of space, but the science 

 of figures in space, possessing the properties of extension and 

 mobility which we find to be common to all material bodies. 

 The question raised here is a very old one, and in a general way 

 its history is familiar. 



Mathematicians have often attempted to construct geometry 

 without the use of what is commonly called the ninth axiom of 

 Euclid, which seems to me best expressed by saying that in a 

 plane only one line can be drawn which shall be parallel to 

 another line in the plane in the sense of never meeting it in 

 either direction. Yet every attempt to construct an elementary 

 geometry without this axiom has been proved to involve a 

 fallacy in some point of the reasoning. This consideration led 

 Lobatchewsky, and independently of him, I believe, Gauss, 

 to inquire whether a geometry might not be constructed in 

 which this axiom did not hold ; in which, in fact, it was pos- 

 sible that if we had two parallel lines in a plane, one of them 

 might turn through a very minute angle without thereby meet- 

 ing the other line in either direction. The possibility of this 

 was soon shown, and a system of geometry was thus constructed 

 in which the sum of the angles of a plane triangle might be less 

 than two right angles. 



Afterward the opposite hypothesis was also introduced. It 

 was found that, given two parallel lines in a plane, it might be 

 supposeJ that they would ultimately meet in both directions. 

 This hypothesis might even be made without there being more 

 than one point of intersection, each straight line returning into 

 itself. The geometry arising from these two hypotheses has 

 been reduced to a rigorous system by Klein. 



To guess the future of mathematical science would be a rash 

 attempt. If made it might seem that, in view of what has been 

 accomplished during our time, the safest course would be to 

 predict great discoveries in this and all other branches of science. 

 The question is sometimes asked whether a mathematical method 

 may not yet be invented which shall be as great an advance on 

 the infinitesimal calculus as the latter was on the methods of 

 Euclid and Diaphuntus. So far as solving problems which now 

 confront us is concerned, I am not sure that the safest course 

 would not be to answer such questions in the negative. Is it 

 1 not true in physics as in mathematics that great discoveries have 

 I been made on unexpected lines, and that the proiilems which 

 perplexed our ancestors now baffle our own efforts? We must 

 jalso remember that the discovery of what could not be done 

 I has been an important element in progress. We are met at 

 jevery step by the iron law of the conservation of energy: in 

 ■ every direction we see the limits of the possible. The mathe- 

 matics of the twenty-first century may be very different from 

 jur own ; perhaps the schoolboy will begin algebra with the 

 heory of substitution-groups, as he might now but for inherited 



abits. Bat we may well doubt whether our posterity will 

 jiolve many problems which we cannot, or invent an algorithm 

 jnore powerful than the calculus. The first principles of all our 

 (uathemaical methods are as old as Euclid, and we cannot ex- 

 pect that the future will do more than apply them to new 

 roblems. 





NO. T266, VOL. 49] 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Oxford. — At a meeting of the Junior Scientific Club, held 

 on Friday, January 26, Mr. Pycraft exhibited a restoration of 

 the wing of archoeopteryx ; Mr. F. A. Hillard read a paper on 

 carborundum, and other substances, prepared by means of the 

 electric arc ; and Mr. H. M. Vernon read a paper on the activity 

 of the cardiac centre under varying conditions. It was agreed 

 at the meeting that the annual Boyle lecture, which will be given 

 this year by Frof. Macalister, should be held early in .May, and 

 that a conversazione should be given on another day in the sum- 

 mer term. 



Cambridge.— Mr. J. W. Capstick, Fellow of Trinity, has 

 been appointed an Assistant Demonstrator in Physics at the 

 Cavendish Laboratory, in the room of Mr. Whetham, who has 

 been elected to the Clerk Maxwell Scholarship. 



A course of lectures with demonstrations in elementary phy- 

 siology for students of agriculture will be given this teim by 

 Mr. Eichholz, Fellow of Emmanuel College, on Mondays and 

 Saturdays, at nine. 



Baron Anatole von Hiigel, Curator of the Museum of 

 Archaeology and Ethnology, will this term give two courses of 

 lectures on the collections in the Museum. 



A syndicate, consisting of the Vice-Chancellor, the Master 

 of Peterhouse, the Master of Christ's, Prof. Thomson, F.R.S., 

 Prof. Liveing, F.R.S., Mr. Glazebrook, F.R.S., and Mr. Shaw, 

 F.R. S., is about to be appointed to consider the best means of 

 extending the Cavendish Laboratory. A site for the extension is 

 reserved, but the standing difficulty of funds is likely to prove 

 a serious one unless outside help can be obtained. 



Dr. P. W. Latham has resigned the Downing Professorship 

 of Medicine, which he has held since 1874. The appointment 

 is made by a special board of electors. Mr. J. R. Green, of 

 Trinity College, Professor of Botany to the Royal Pharmaceu- 

 tical Society of Great Britain, has been approved by the General 

 Board of Studies for the degree of Doctor of Science. 



It is proposed to admit to the privileges of affiliated students, 

 matriculated members of the University of Adelaide who have 

 studied there for two years in arts, law, science, or medicine, 

 and have passed certain specified examinations. Such affiliated 

 students are exempted from the Previous Examination and from 

 one year of residence for the B.A. degree. 



SCIENTIFIC SERIALS. 



American Meteorological Journal, ]z.nViZ.xy. — History of the 

 Weather Map, by M. W. Harrington. Simultaneous observ- 

 ations, which form the basis of weather charts, were made in 

 Virginia from 1772 to 1777; about the same time Lavoisier 

 proposed that such observations should be made in Europe, and 

 referred to an earlier proposal by Borda. In 1842, Kreil, of 

 Prague, proposed the use of an electromagnetic telegraph for 

 the same purpose. The earliest proposal for a weather map was 

 probably made by Brandes, in 1S16, but his plan seems never 

 to have been carried out, and it was not until 1856 that current 

 charts of the weather were made by the Smithsonian Insti- 

 tution. In 1857, Le Verrier published an international bulletin, 

 but his synoptic charts were not issued until 1863 ; and in this 

 country Admiral FitzRoy commenced the publication of tele- 

 graphic weather reports in i860; since this time such reports 

 and charts became general.— The meteorological work of the 

 Medical Department of the United States Army, by Major C. 

 Smart. The earliest meteorological journal in the office of the 

 Surgeon-General is from Cambridge, for July, 1816. The first 

 results were published in the Meteorological Register for the 

 years 1822-5.— The meteorological work of the Smithsonian 

 Institution, by S. P. Langley. In December, 1847, Prof. J. 

 Henry proposed a "system of extended meteorological observ- 

 ations for solving the problem of American storms, and 

 shortly afterwards the institution issued directions for meteoro- 

 logical observations ; in 1849 elementary telegraphic weather 

 reports were furnished to the institution daily.— Early indi- 

 vidual observers in the United Slates, by A. J. Henry, A daily 

 record of the weather was kept by the Rev. J. Campanius at 

 Fort Christiania, near the present city of Wilmington, Dela- 

 ware, during 1644-5, and at Boston, by the Hon. P. Dudley, in 



